I'm such an idiot. I figured out there were 10 kids on the right, and then figured out there were 6 kids before the 7th kid on the left, and hence 4 kids after the 18th kid to the left, for a total of 18 + 4 = 22 kids.

The question may be considered by solving a simpler problem. If 4 kids stand in a circle, 1 is opposite 3 and 2 is opposite 4. The difference in position is always 2. Double it to find the number.
So 18 - 7 = 11. 2 * 11 = 22.